Aims . We aim to revisit the formation pathway of AB Pic b, an imaged companion that straddles the exoplanet/brown-dwarf boundary. We based this study on a rich set of observations, which allows us to investigate its orbital and atmospheric properties. Methods . We composed a spectrum of AB Pic b by merging archival medium-resolution (~4000) VLT/SINFONI K band (1.96–2.45 µm) data with published spectra at J and H bands from SINFONI, Lp band from Magellan-AO/CLIO2, and photometric measurements from HST (visible) and Spitzer (mid-infrared). We modeled the spectrum with ForMoSA, following a forward-modeling approach based on two atmospheric models: ExoREM and BT-SETTL13. In parallel, we determined the orbital properties of AB Pic b fitting orbital solutions to astrometric measurements from NaCo (2003 and 2004) and SPHERE (2015). Results . The orbital solutions favor a semi-major axis of 190 -50 +200 au on a highly inclined orbit (edge-on), but with a poorly constrained eccentricity. From the atmospheric modeling with Exo-REM, we derive an effective temperature of 1700 ± 50 K and surface gravity of 4.5 ± 0.3 dex, which are consistent with previous findings, and we report for the first time a c/o ratio of 0.58 ± 0.08, consistent with the value for the Sun. The posteriors are sensitive to the wavelength interval and the family of models used. Given the published rotation period of 2.1 h and our derived υ sin( i ) of 73 -27 +11 km s −1 , we estimate for the first time the true obliquity of AB Pic b to be between 45 and 135 deg, indicating a rather significant misalignment between the spin and orbit orientations of the planet. Finally, the existence of a proper-motion anomaly between the H IPPARCOS and Gaia Early Data Release 3 compared to our SPHERE detection limits and adapted radial velocity limits indicates the potential existence of a ~6 M Jup inner planet orbiting from 2 to 10 au (40–200 mas). Conclusions . The possible existence of an inner companion and the likely misalignment of the spin-axis orientation strongly favor a formation path by gravitational instability or core accretion within a protoplanetary disk at a smaller orbital radius followed by a dynamical interaction which scattered AB Pic b to its current location. Confirmation and characterization of this unseen inner exoplanet and access to a broader wavelength coverage and higher spectral resolution for the characterization of AB Picb will be essential for probing the uncertainties associated with the atmospheric and orbital parameters.